EST

Expanding Spacetime Theory

Justifying the EST theory

Three levels of scientific inquiry

There are three levels of scientific inquiry corresponding to deepening levels of
understanding.

At the first level the question is: “What?”. What is the nature of a
certain phenomena or objects under investigation? How do we recognize and classify
them? In the past this was the traditional scientific activity, for example the
identification, classification and counting of various species.

At the second level the question becomes “How?” We want to know how
certain processes work or how certain species evolved and their relationship to
the environment. This is the current level of inquiry in many disciplines where
the emphasis is trying to understand the relationship between phenomena rather than
just classify and characterize them.

At the deepest level of inquiry the question is: “Why?”. We want to
know not just the “hows” of a certain phenomena but why it exists in
Nature. Many consider this question to be meta-physical outside the realm of scientific
inquiry. But this deeper question has inspired some of the greatest thinkers throughout
history. Einstein used to ask himself if the Lord had any options in designing the
world or if there are other equally viable possibilities. Although many scientists
might not seriously ponder why things are what they are, most are driven by a desire
to better understand the world we live in. It is my belief that our inquiry will
not end until we will be able to answer the Why question.

The EST theory takes a tiny step in this direction. It is based on a few fundamental
principles and if these principles hold true they would explain why the universe
looks and behaves the way it does. For example, they would explain what causes the
progression of time, how it is implemented by Nature and also give a tentative answer
to why time progresses. It also tells us why the quantum mechanical world exists.

Three postulates

The philosophical line of reasoning that leads to the EST theory starts with the
proposition that the cosmological scale of material object and dynamic processes
is a relative concept and that no absolute scale of things exists in the universe.
The scale of material objects (the spatial scale) and the duration of fundamental
processes (the temporal scale), for example the period of a spectral line frequency,
may only be defined in relation to other objects and processes. This relativity
of scale not only makes intuitive sense, since it is difficult to understand why
any particular scale should take preference if the universe is all there is, but
also is in agreement with theoretical physics, which recognizes scale invariance
as a well known example of gauge invariance.

Therefore, I will make universal scale invariance my first postulate:

P1: There is no absolute scale of matter and dynamic processes.

However, in general relativity this gauge invariance seems quite trivial since a
different scale may be though of as simply a re-definition of the metrics of spacetime
so that different scales merely correspond to different units of measurement. Although
this is true if the scale remains constant, the discovery of the cosmological expansion
raises the question whether the cosmological scale might change with time. Such
an expanding scale would have real physical effects and create a universe with different
properties compared to a cosmos with fixed scale. Since general relativity does
not distinguish between different scales and since there seem to be no reason why
any particular scale should take preference it appears reasonable to assume that
if the universe expands by changing the scale both of space and time, different
epochs are geometrically and physically equivalent. This reasoning leads to the
second postulate:

P2: All spatial and temporal locations are physically equivalent in all respects.

If the scale of both space and time increase we could attempt to model this in GR
by a time dependent scale factor, a(t), multiplying all four metrics in the
line element. This would model a universe where spacetime expands relative to a
fictitious coordinate system with fixed rate of (proper) time as given by the invariant
ds. Based on the two postulates above we conclude that the cosmological scale
expansion must be exponential with time. In this case different epochs are equivalent
because a line element with the scale a(t) is for some constant increment
Δt equivalent to one with scale a(t+ Δt). In other words,
the line element with scale factor exp(t) is equivalent to the line element
with scale factor exp(t+Δt) = constant·exp(t) since spacetimes differing
by a constant scale factor are equivalent according to general relativity. Thus,
different epochs are physically equivalent. However, this equivalence can only be
obtained between spacetimes of differing scales corresponding to some time increment
Δt. These two line elements are related via the simple transformation
t2= t1+ Δt and therefore strongly
equivalent in the sense of Einstein. No continuous variable transformation exists
relating different line elements with scale factors exp( t1) and exp(t2).
This suggests that the requirement that all epochs are equivalent (covariant) in
the sense of Einstein implies that the cosmological expansion must occur in discrete
temporal increments. We thus arrive at a third postulate:

P3: The cosmological expansion takes place in discrete temporal increments.

Together these three postulates form the basis for the Expanding Spacetime theory.
The third postulate also follows from the impossibility of conceiving a pace of
time that accelerates relative to itself. Introducing the expanding cosmological
scale as a “fifth dimension” beyond the four dimensions of spacetime
in the EST theory circumvents this difficulty.

The search for symmetry is central to modern theories in physics. The word symmetry
is here used in a special sense; it denotes invariance under various (group) transformations.
For example, the laws of physics are invariant under translations in space and time.
An observer in a “galaxy far, far away” in the past or in the future
would find the laws that of physics are the same. There also is rotational symmetry;
there is no physical difference between different directions in space. But, one
symmetry is most fundamental of all - scale invariance. This symmetry preserves
everything including the four-dimensional spacetime of general relativity.
Since all laws of physics are expressed by general relativity, this symmetry preserves
all laws of physics. It preserves the world. We might perhaps call it the mother
of all symmetries. Therefore, it should come as no a surprise that the most fundamental
property of the universe, the progression of time, is based on this fundamental
symmetry.

If we model the cosmological scale expansion by a line element with an exponentially
increasing scale factor relative to a fictitious non-expanding coordinate system,
how could this be modeled in a coordinate system that expands together with spacetime?
For an observer in this expanding spacetime the relationship between the metrics
of space and time would always remain the same but there would be additional physical
effects due the exponentially accelerating scale. At every instant t= Δt
the universe would “look the same” as it did at t=0. One possible
way of modeling this mode of expansion is the following iteration:

Spacetime expands from t to t+ Δt by changing the scale factor
from exp(t/T) to exp[(t+Δt)/T].

At t+Δt the pace of proper time suddenly slows down by changing the
invariant increment ds => ds·exp(Δt/T).

The factor exp(Δt/T) now appears on both sides of the line element
and may be eliminated restoring the line element with scale factor exp(t/T)
in step 1 above.

The iteration loops back to step 1.

The new and radically different aspect of this cosmological expansion mode is the
discrete change of the pace of time in step 2. This takes the EST model beyond GR
and established epistemology, which presumes continuous processes. One may well
wonder if this radical departure is justified.

The nature of motion

The nature of “motion” has been contemplated for millenniums. How does
a moving particle change its position with time? This was an unresolved mystery
for the antique Greeks, but since the seventeenth century, with the introduction
of differential calculus, we treat motion as a limiting process of infinitely many
incremental, diminutive, steps. Since this works excellently when modeling macroscopic
motion, the dynamics of moving objects is since the seventeenth century generally
treated by solving differential equations assuming a continuous progression of time.

Although with take the validity of continuous motion for granted, upon deeper reflection
this idea seems rather strange. In fact, it is difficult if not impossible to think
of motion as a continuous process. We always tend to visualize motion as a sequence
of small displacements. The difficulty with continuous motion is that it implies
that an infinite number of steps must occur in a very short time. The ancient Greeks
recognized this puzzle as one of Zeno’s paradoxes. More recently the same
problem has reappeared in the context of quantum theory since it appears that the
nature of the quantum world is discrete rather than continuous.

The very natural idea of moving by a sequence of consecutive steps might actually
be the way Nature implements motion. Continuous motion might never occur in Nature.
It is not unlikely that the notion of a continuous physical process is a human idea
supported by a mathematical representation, differential calculus, without corresponding
physical reality. The nature of the progression of time might very well be discrete,
and the modeling of dynamic processes by differential equations might fail in the
quantum world.

In addition to this philosophical argument I offer the following comments:

To begin with, the EST model, which is based on a discrete progression of time,
better agrees with astronomical observations than the Big Bang model and it resolves
several cosmological puzzles. It also predicts a new phenomenon, Cosmic Drag, which
explains the spiral form of galaxies and recently might have been verified by direct
observations in the solar system.

Second, philosophically there is nothing wrong with the assumption that the scale
of the universe might change with time and that all epochs are equivalent. Everyone
will easily grasp this cosmological expansion mode. However, such a continuous scale
expansion process cannot be modeled (covariantly) by GR and has therefore not been
seriously considered in the past. But, we ought to be able to model a cosmological
scale that expands with time. The fact that we cannot do this indicates a weakness
in available mathematical models rather than a constraint to be imposed on the way
the universe works. In short, the fact that we cannot model it does not mean that
it cannot be.

Third, quantum mechanics and GR, the two dominant theories of the twentieth century,
are incompatible, which shows that something important is missing in our understanding.
Either one, or perhaps both, of these theories are incomplete. I believe that GR
is incomplete in that it cannot model the quantum world since it excludes the possibility
of a discrete evolution of time. It appears that GR could be generalized by including
discrete gauge transformations that do not change the energy-momentum tensor. I
also believe that our understanding of the quantum world is incomplete, since we
have not been able to give a physical explanation to the wave functions.

Fourth, quantum mechanical representation of fields leads to infinities in the calculations.
Some of these problems may be handled by ugly ad hoc “normalization”
techniques but others remain. We know that this deficiency in the theory must be
due to lacking insight into the nature of matter and spacetime. Again, something
really important is missing. If the problem were superficial it would have been
resolved long ago. Since it still remains it indicates that a problem must exist
at some deep level. I believe that the problem lies in the modeling of spacetime
as a continuous manifold and motion as a continuous process.

These shortcomings of modern physics clearly show that our current understanding
is inadequate and that we must find a way out of the constraints imposed by accepted
epistemology. Such a step necessarily must take us outside known science and may
therefore initially be considered “unscientific”. Unfortunately, this
also means that any attempt made in this direction initially will be rejected by
the main body of a scientific establishment who typically defines “science”
as being comprised of the already known.

But, soon a new generation will break the constraints of traditional epistemology
finding solutions to many currently unresolved problems.